About the embedding of Teichmüller space in the space of geodesic Hölder distributions

Abstract

In the first section, we review the construction due to L. Bers of the complex structure on the Teichmüller space of a Fuchsian group. Then we recall the definition of the space of Hölder distributions on the space of geodesics of ℍ2, introduced by F. Bonahon for cocompact Fuchsian groups. This definition was recently extended to the case of general Fuchsian groups by D. Šarić who showed that the Liouville map embeds the Teichmüller space into the space of geodesic Hölder distributions. We show that this embedding is analytic.